A335191 - OEIS

A335191

Number of Heronian triangles with perimeter A335103(n) whose smallest side length is a square.

1, 2, 1, 3, 3, 2, 1, 1, 1, 1, 1, 2, 1, 5, 2, 5, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 7, 5, 3, 1, 5, 1, 1, 5, 3, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 5, 1, 4, 1, 1, 1, 8, 5, 1, 3, 2, 1, 1, 1, 3, 6, 3, 2, 2, 3, 2, 1, 1, 2, 1, 3, 3, 4, 1, 1, 1, 3, 1, 2, 1, 3, 4, 2, 2, 1, 1, 7, 1, 2, 7, 1, 1

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..95.

Eric Weisstein's World of Mathematics, Heronian Triangle

Wikipedia, Heronian triangle

Wikipedia, Integer Triangle

FORMULA

a(n) = Sum_{k=1..floor(b(n)/3)} Sum_{i=k..floor((b(n)-k)/2)} sign(floor((i+k)/(b(n)-i-k+1))) * chi(sqrt((b(n)/2)*(b(n)/2-i)*(b(n)/2-k)*(b(n)/2-(b(n)-i-k)))) * c(k), where chi(n) = 1 - ceiling(n) + floor(n), c is the square characteristic (A010052) and b = A335103.

EXAMPLE

a(1) = 1; There is one Heronian triangle with perimeter A335103(1) = 32 whose smallest side length is a square, [4,13,15].

CROSSREFS

Cf. A010052, A335103, A335208, A335211.

Sequence in context: A330694 A088074 A071463 * A342718 A355686 A308530

Adjacent sequences: A335188 A335189 A335190 * A335192 A335193 A335194

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 26 2020

STATUS

approved